**Answer:**

Option E

**Explanation:**

**II.** $A$’s $1$ hour work $=\frac{1}{16}$.

Suppose $B$ fills the tank in $x$ hours. Then, $B$’s $1$ hour work $=\frac{1}{x}$.

**I.** Work done by $A$ in $1$ hour $=150\%$ of $\frac{1}{x}$ $=\left(\frac{1}{x}\times\frac{150}{100}\right)$ $=\frac{3}{2x}$.

$\therefore\frac{3}{2x}=\frac{1}{16}$

$\Leftrightarrow x=24$.

So, $B$ can fill the tank in 24 hours.

$(A+B)$’s $1$ hour work $=\left(\frac{1}{16}+\frac{1}{24}\right)$ $=\frac{5}{48}$.

$\therefore $ $(A+B)$ can fill the tank in $\frac{48}{5}$ hrs.

Thus I & II give the answer.

**III. **Work done by $B$ in $1$ hour $=\frac{1}{24}$.

From II & III, we get the same answer.

From III & I, we get :

$A$’s $1$ hour work $=150\%$ of $\frac{1}{24}$ $=\left(\frac{1}{24}\times\frac{150}{100}\right)$ $=\frac{1}{16}$.

Thus, III & I, we get the answer.

$\therefore$ Correct answer is **(E)**.